Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes

Observation of Topological Transition in Floquet Non-Hermitian Skin Effects in Silicon Photonics

Non-Hermitian physics has greatly enriched our understanding of nonequilibrium phenomena and uncovered novel effects such as the non-Hermitian skin effect (NHSE) that has profoundly revolutionized the field. NHSE has been predicted in systems with nonreciprocal couplings which, however, are challenging to realize in experiments. Without nonreciprocal couplings, the NHSE can also emerge in systems with coexisting gauge fields and loss or gain (e.g., in Floquet non-Hermitian systems). However, such Floquet NHSE remains largely unexplored in experiments. Here, we realize the Floquet NHSEs in periodically modulated optical waveguides integrated on a silicon photonic platform. By engineering the artificial gauge fields induced by the periodical modulation, we observe various Floquet NHSE phases and unveil their rich topological transitions. Remarkably, we discover the transitions between the unipolar NHSE phases and an unconventional bipolar NHSE phase, which is accompanied by the directional reversal of the NHSEs. The underlying physics is revealed by the band winding in complex quasienergy space which undergoes a topology change from isolated loops with the same winding to linked loops with opposite windings. Our work unfolds a new route toward Floquet NHSEs originating from the interplay between gauge fields and dissipation effects, and thus offers fundamentally new ways for steering light and other waves.

Topologically protected entanglement switching around exceptional points

The robust operation of quantum entanglement states is crucial for applications in quantum information, computing, and communications1-3. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.

Chiral quantum heating and cooling with an optically controlled ion

Quantum heat engines and refrigerators are open quantum systems, whose dynamics can be well understood using a non-Hermitian formalism. A prominent feature of non-Hermiticity is the existence of exceptional points (EPs), which has no counterpart in closed quantum systems. It has been shown in classical systems that dynamical encirclement in the vicinity of an EP, whether the loop includes the EP or not, could lead to chiral mode conversion. Here, we show that this is valid also for quantum systems when dynamical encircling is performed in the vicinity of their Liouvillian EPs (LEPs), which include the effects of quantum jumps and associated noise-an important quantum feature not present in previous works. We demonstrate, using a Paul-trapped ultracold ion, the first chiral quantum heating and refrigeration by dynamically encircling a closed loop in the vicinity of an LEP. We witness the cycling direction to be associated with the chirality and heat release (absorption) of the quantum heat engine (quantum refrigerator). Our experiments have revealed that not only the adiabaticity breakdown but also the Landau-Zener-Stückelberg process play an essential role during dynamic encircling, resulting in chiral thermodynamic cycles. Our observations contribute to further understanding of chiral and topological features in non-Hermitian systems and pave a way to exploring the relation between chirality and quantum thermodynamics.

Dynamically Encircling Exceptional Points in Different Riemann Sheets for Orbital Angular Momentum Topological Charge Conversion

Orbital angular momentum (OAM) provides an additional degree of freedom for optical communication systems, and manipulating on-chip OAM is important in integrated photonics. However, there is no effective method to realize OAM topological charge conversion on chip. In this Letter, we propose a way to convert OAM by encircling two groups of exceptional points in different Riemann sheets. In our framework, any OAM conversion can be achieved on demand just by manipulating adiabatic and nonadiabatic evolution of modes in two on-chip waveguides. More importantly, the chiral OAM conversion is realized, which is of great significance since the path direction can determine the final topological charge order. Our Letter presents a special chiral behavior and provides a new method to manipulate OAM on the chip.

Dynamical encircling of multiple exceptional points in anti-PT symmetry system

Exceptional points (EPs) in non-Hermitian systems have turned out to be at the origin of many intriguing effects with no counterparts in Hermitian cases. A typically interesting behavior is the chiral mode switching by dynamically winding the EP. Most encircling protocols focus on the two-state or parity-time (PT) symmetry systems. Here, we propose and investigate the dynamical encircling of multiple EPs in an anti-PT-symmetric system, which is constructed based on a one-dimensional lattice with staggered lossy modulation. We reveal that dynamically encircling the multiple EPs results in the chiral dynamics via multiple non-Hermiticity-induced nonadiabatic transitions, where the output state is always on the lowest-loss energy sheet. Compared with the PT-symmetric systems that require complicated variation of the gain/loss rate or on-site potentials, our system only requires modulations of the couplings which can be readily realized in various experimental platforms. Our scheme provides a route to study non-Hermitian physics by engineering the EPs and implement novel photonic devices with unconventional functions.

Omni-polarized Faraday isolator based on non-Hermitian Faraday system

Non-Hermitian systems have recently attracted significant attention in photonics due to the realization that the interplay between gain and loss can lead to entirely new and unexpected features. Here, we propose and demonstrate a non-Hermitian Faraday system capable of non-reciprocal omni-polarizer action at the exceptional point. Notably, both forward and backward propagating light with arbitrary polarization converge to the same polarization state. Leveraging the robustness and non-reciprocity of the non-Hermitian Faraday system, we realize an omni-polarized Faraday isolator that can effectively isolate any polarized light without the need for a polarizer at the incident port of backward propagation. Remarkably, under the given parameter configuration, the isolator achieves a maximum isolation ratio of approximately 100 dB and a minimum isolation ratio of around 45 dB for various polarized light, accompanied by near-zero insertion loss. Furthermore, our research reveals the remarkable tolerance of the non-Hermitian Faraday isolator to nonlinear effects. This unique characteristic allows us to harness nonlinear effects to achieve various optical functions, all while maintaining excellent isolation performance. The proposed non-Hermitian Faraday system paves the way for the realization of magnetically or optically switchable non-reciprocal devices.

Observation of non-Hermitian skin effect in thermal diffusion

The paradigm shift of Hermitian systems into the non-Hermitian regime profoundly modifies inherent property of the topological systems, leading to various unprecedented effects such as the non-Hermitian skin effect (NHSE). In the past decade, the NHSE has been demonstrated in quantum, optical and acoustic systems. Beside those wave systems, the NHSE in diffusive systems has not yet been observed, despite recent abundant advances in the study of topological thermal diffusion. In this work, we design a thermal diffusion lattice based on a modified Su-Schrieffer-Heeger model and demonstrate the diffusive NHSE. In the proposed model, the asymmetric temperature field coupling inside each unit cell can be judiciously realized by appropriate configurations of structural parameters. We find that the temperature fields trend to concentrate toward the target boundary which is robust against initial excitation conditions. We thus experimentally demonstrated the NHSE in thermal diffusion and verified its robustness against various defects. Our work provides a platform for exploration of non-Hermitian physics in the diffusive systems, which has important applications in efficient heat collection, highly sensitive thermal sensing and others.

Chiral transmission by an open evolution trajectory in a non-Hermitian system

Exceptional points (EPs), at which two or more eigenvalues and eigenstates of a resonant system coalesce, are associated with non-Hermitian Hamiltonians with gain and/or loss elements. Dynamic encircling of EPs has received significant interest in recent years, as it has been shown to lead to highly nontrivial phenomena, such as chiral transmission in which the final state of the system depends on the encircling handedness. Previously, chiral transmission for a pair of eigenmodes has been realized by establishing a closed dynamical trajectory in parity-time- (PT-) or anti-PT-symmetric systems. Although chiral transmission of symmetry-broken modes, more accessible in practical photonic integrated circuits, has been realized by establishing a closed trajectory encircling EPs in anti-PT-symmetric systems, the demonstrated transmission efficiency is very low due to path-dependent losses. Here, we demonstrate chiral dynamics in a coupled waveguide system that does not require a closed trajectory. Specifically, we explore an open trajectory linking two infinite points having the same asymptotic eigenmodes (not modes in PT- and anti-PT-symmetric systems), demonstrating that this platform enables high-efficiency chiral transmission, with each eigenmode localized in a single waveguide. This concept is experimentally implemented in a coupled silicon waveguide system at telecommunication wavelengths. Our work provides a new evolution strategy for chiral dynamics with superior performance, laying the foundation for the development of practical chiral-transmission devices.

Observation of Nonlinear Exceptional Points with a Complete Basis in Dynamics

The exotic physics associated with exceptional points (EPs) is always under the scrutiny of theoretical and experimental science. Recently, considerable effort has been invested in the combination of nonlinearity and non-Hermiticity. The concept of nonlinear EPs (NEPs) has been introduced, which can avoid the loss of completeness of the eigenbasis in dynamics while retaining the key features of linear EPs. Here, we present the first direct experimental demonstration of a NEP based on two non-Hermition coupled circuit resonators combined with a nonlinear saturable gain. At the NEP, the response of the eigenfrequency to perturbations demonstrates a third-order root law and the eigenbasis of the Hamiltonian governing the system dynamics is still complete. Our results bring this counterintuitive aspect of the NEP to light and possibly open new avenues for applications.

Dissipative coupling in a Bragg-grating-coupled single resonator with Fano resonance for anti-PT-symmetric gyroscopes

Anti-parity-time-symmetric Hamiltonians show an enhanced sensitivity to external perturbations that can be used for high-performance angular velocity sensing. Dissipative coupling is a valuable way for realizing anti-PT-symmetric Hamiltonians with optical resonators and is usually obtained by means of auxiliary waveguides. Here, we model and experimentally show the dissipative coupling between two counterpropagating modes of a single resonator, by means of a Bragg-grating placed in the feeding bus. The proposed solution enables the possibility of accurately designing the dissipative coupling strength in integrated non-Hermitian gyroscopes, thus providing high flexibility in the design of the proposed sensor. Moreover, we theoretically and experimentally demonstrate that the dissipative coupling between two counterpropagating modes of the same resonant cavity can give rise to an asymmetric Fano resonance.

Electrically tunable topological phase transition in non-Hermitian optical MEMS metasurfaces

Exceptional points (EPs), unique junctures in non-Hermitian open systems where eigenvalues and eigenstates simultaneously coalesce, have gained notable attention in photonics because of their enthralling physical principles and unique properties. Nonetheless, the experimental observation of EPs, particularly within the optical domain, has proven rather challenging because of the grueling demand for precise and comprehensive control over the parameter space, further compounded by the necessity for dynamic tunability. Here, we demonstrate the occurrence of optical EPs when operating with an electrically tunable non-Hermitian metasurface platform that synergizes chiral metasurfaces with piezoelectric MEMS mirrors. Moreover, we show that, with a carefully constructed metasurface, a voltage-controlled spectral space can be finely tuned to access not only the chiral EP but also the diabolic point characterized by degenerate eigenvalues and orthogonal eigenstates, thereby allowing for dynamic topological phase transition. Our work paves the way for developing cutting-edge optical devices rooted in EP physics and opening uncharted vistas in dynamic topological photonics.

Transient Loss-Induced Non-Hermitian Degeneracies for Ultrafast Terahertz Metadevices

Non-Hermitian degeneracies, also known as exceptional points (EPs), have attracted considerable attention due to their unique physical properties. In particular, metasurfaces related to EPs can open the way to unprecedented devices with functionalities such as unidirectional transmission and ultra-sensitive sensing. Herein, an active non-Hermitian metasurface with a loss-induced parity-time symmetry phase transition for ultrafast terahertz metadevices is demonstrated. Specifically, the eigenvalues of the non-Hermitian transmission matrix undergo a phase transition under optical excitation and are degenerate at EPs in parameter space, which is accompanied by the collapse of chiral transmission. Ultrafast EP modulation on a picosecond time scale can be realized through variations in the transient loss at a non-Hermitian metasurface pumped by pulsed excitation. Furthermore, by exploiting the physical characteristics of chiral transmission EPs, a switchable quarter-wave plate based on the photoactive metasurface is designed and experimentally verified and realized the corresponding function of polarization manipulation. This work opens promising possibilities for designing functional terahertz metadevices and fuses EP physics with active metasurfaces.

Enhanced Sensing Mechanism Based on Shifting an Exceptional Point

Non-Hermitian systems associated with exceptional points (EPs) are expected to demonstrate a giant response enhancement for various sensors. The widely investigated enhancement mechanism based on diverging from an EP should destroy the EP and further limits its applications for multiple sensing scenarios in a time sequence. To break the above limit, here, we proposed a new enhanced sensing mechanism based on shifting an EP. Different from the mechanism of diverging from an EP, our scheme is an EP nondemolition and the giant enhancement of response is acquired by a slight shift of the EP along the parameter axis induced by perturbation. The new sensing mechanism can promise the most effective response enhancement for all sensors in the case of multiple sensing in a time sequence. To verify our sensing mechanism, we construct a mass sensor and a gyroscope with concrete physical implementations. Our work will deepen the understanding of EP-based sensing and inspire designing various high-sensitivity sensors in different physical systems.

Scattering exceptional point in the visible

Exceptional point (EP) is a special degeneracy of non-Hermitian systems. One-dimensional transmission systems operating at EPs are widely studied and applied to chiral conversion and sensing. Lately, two-dimensional systems at EPs have been exploited for their exotic scattering features, yet so far been limited to only the non-visible waveband. Here, we report a universal paradigm for achieving a high-efficiency EP in the visible by leveraging interlayer loss to accurately control the interplay between the lossy structure and scattering lightwaves. A bilayer framework is demonstrated to reflect back the incident light from the left side ( | r-1 | >0.999) and absorb the incident light from the right side ( | r+1 | < 10-4). As a proof of concept, a bilayer metasurface is demonstrated to reflect and absorb the incident light with experimental efficiencies of 88% and 85%, respectively, at 532 nm. Our results open the way for a new class of nanoscale devices and power up new opportunities for EP physics.

Exceptional points and non-Hermitian photonics at the nanoscale

Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl exceptional rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss the constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic applications.

Non-Hermitian Chiral Heat Transport

Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.

Observation of Exceptional Points in Thermal Atomic Ensembles

Exceptional points (EPs) in non-Hermitian systems have recently attracted wide interest and spawned intriguing prospects for enhanced sensing. However, EPs have not yet been realized in thermal atomic ensembles, which is one of the most important platforms for quantum sensing. Here we experimentally observe EPs in multilevel thermal atomic ensembles and realize enhanced sensing of the magnetic field for 1 order of magnitude. We take advantage of the rich energy levels of atoms and construct effective decays for selected energy levels by employing laser coupling with the excited state, yielding unbalanced decay rates for different energy levels, which finally results in the existence of EPs. Furthermore, we propose the optical polarization rotation measurement scheme to detect the splitting of the resonance peaks, which makes use of both the absorption and dispersion properties and shows an advantage with enhanced splitting compared with the conventional transmission measurement scheme. Additionally, in our system both the effective coupling strength and decay rates are flexibly adjustable, and thus the position of the EPs are tunable, which expands the measurement range. Our Letter not only provides a new controllable platform for studying EPs and non-Hermitian physics, but also provide new ideas for the design of EP-enhanced sensors and opens up realistic opportunities for practical applications in the high-precision sensing of magnetic field and other physical quantities.

Nonlinear Exceptional Points with a Complete Basis in Dynamics

Exceptional points (EPs) are special spectral singularities at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become identical. In conventional wisdom, the coalescence of eigenvectors inevitably leads to the loss of completeness of the eigenbasis. Here, we show that this scenario breaks down in general at nonlinear EPs (NEPs). As an example, we realize a fifth-order NEP (NEP_{5}) within only three coupled resonators with both a theoretical model and simulations in circuits. One stable and another four auxiliary steady eigenstates of the nonlinear Hamiltonian coalesce at the NEP_{5}, and the response of eigenfrequency to perturbations demonstrates a fifth-order root law. Intriguingly, the biorthogonal eigenbasis of the Hamiltonian governing the system dynamics is still complete, and this fact is corroborated by a finite Petermann factor instead of a divergent one at conventional EPs. Consequently, the amplification of noise, which diverges at other EPs, converges at our NEP_{5}. Our finding transforms the understanding of EPs and shows potential for miniaturizing various key applications operating near EPs.

Generation of an ultrashort pulse train through ultrafast parity-time symmetry switching

We propose a scheme for the direct generation of an ultrashort pulse train as well as the further compression of pulsed lasers based on the nonlinearity inherent to parity-time (PT) symmetric optical systems. Implementation of optical parametric amplification in a directional coupler of χ⁽²⁾ waveguides enables ultrafast gain switching through pump-controlled breaking of PT symmetry. We theoretically demonstrate that pumping such a PT symmetric optical system with a periodically amplitude-modulated laser enables periodic gain switching, which can directly convert a continuous-wave signal laser into a train of ultrashort pulses. We further demonstrate that by engineering the PT symmetry threshold, an apodized gain switching that enables the production of ultrashort pulses without side lobes. This work suggests a new approach for exploring the non-linearity inherent to various PT symmetric optical structures to extend optical manipulation capabilities.

Theoretical investigation of dynamics and concurrence of entangled [Formula: see text] and anti-[Formula: see text] symmetric polarized photons

Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.

Graphene metasurface hits the point

Exceptional points pose exceptional difficulties to access and encircle. By simply gating graphene, it is now easier to hit the exceptional point.

Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

Nontrivial spectral properties of non-Hermitian systems can lead to intriguing effects with no counterparts in Hermitian systems. For instance, in a two-mode photonic system, by dynamically winding around an exceptional point (EP) a controlled asymmetric-symmetric mode switching can be realized. That is, the system can either end up in one of its eigenstates, regardless of the initial eigenmode, or it can switch between the two states on demand, by simply controlling the winding direction. However, for multimode systems with higher-order EPs or multiple low-order EPs, the situation can be more involved, and the ability to control asymmetric-symmetric mode switching can be impeded, due to the breakdown of adiabaticity. Here we demonstrate that this difficulty can be overcome by winding around exceptional curves by additionally crossing diabolic points. We consider a four-mode [Formula: see text]-symmetric bosonic system as a platform for experimental realization of such a multimode switch. Our work provides alternative routes for light manipulations in non-Hermitian photonic setups.

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems

We study the enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric, with the two involved cavities being dissipatively coupled via the waveguide. The anti-PT symmetry may break down when a weak waveguide-mediated coherent coupling is introduced. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity measured by an enhancement factor is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the enhancement factor shows resistance to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength and has potential applications in high-precision measurements with systems involving Kerr-type nonlinearity.

Harnessing Dynamical Encircling of an Exceptional Point in Anti-PT-Symmetric Integrated Photonic Systems

Dynamically encircling an exceptional point in a non-Hermitian system can lead to chiral behaviors, but this process is difficult for on-chip PT-symmetric devices which require accurate control of gain and loss rates. Here, we experimentally demonstrated encircling an exceptional point with a fixed loss rate in a compact anti-PT-symmetric integrated photonic system, where chiral mode switching was achieved within a length that is an order of magnitude shorter than that of a PT-symmetric system. Based on the experimental demonstration, we proposed a topologically protected mode (de)multiplexer that is robust against fabrication errors with a wide operating wavelength range. With the advantages of simplified fabrication and characterization processes, the demonstrated system can be used for studying higher-order exceptional points and for exotic light manipulation.

Radiative anti-parity-time plasmonics

Space and guided electromagnetic waves, as widely known, are two crucial cornerstones in extensive wireless and integrated applications respectively. To harness the two cornerstones, radiative and integrated devices are usually developed in parallel based on the same physical principles. An emerging mechanism, i.e., anti-parity-time (APT) symmetry originated from non-Hermitian quantum mechanics, has led to fruitful phenomena in harnessing guided waves. However, it is still absent in harnessing space waves. Here, we propose a radiative plasmonic APT design to harness space waves, and experimentally demonstrate it with subwavelength designer-plasmonic structures. We observe two exotic phenomena unrealized previously. Rotating polarizations of incident space waves, we realize polarization-controlled APT phase transition. Tuning incidence angles, we observe multi-stage APT phase transition in higher-order APT systems, constructed by using the scalability of leaky-wave couplings. Our scheme shows promise in demonstrating novel APT physics, and constructing APT-symmetry-empowered radiative devices.

Experimental realization of non-Abelian permutations in a three-state non-Hermitian system

Eigenstates of a non-Hermitian system exist on complex Riemannian manifolds, with multiple sheets connecting at branch cuts and exceptional points (EPs). These eigenstates can evolve across different sheets-a process that naturally corresponds to state permutation. Here, we report the first experimental realization of non-Abelian permutations in a three-state non-Hermitian system. Our approach relies on the stroboscopic encircling of two different exceptional arcs (EAs), which are smooth trajectories of order-2 EPs appearing from the coalescence of two adjacent states. The non-Abelian characteristics are confirmed by encircling the EAs in opposite sequences. A total of five non-trivial permutations are experimentally realized, which together comprise a non-Abelian group. Our approach provides a reliable way of investigating non-Abelian state permutations and the related exotic winding effects in non-Hermitian systems.

Efficient second harmonic generation by harnessing bound states in the continuum in semi-nonlinear etchless lithium niobate waveguides

Integrated photonics provides unprecedented opportunities to pursue advanced nonlinear light sources with low-power consumptions and small footprints in a scalable manner, such as microcombs, chip-scale optical parametric oscillators and integrated quantum light sources. Among a variety of nonlinear optical processes, high-efficiency second harmonic generation (SHG) on-chip is particularly appealing and yet challenging. In this work, we present efficient SHG in highly engineerable semi-nonlinear waveguides consisting of electron-beam resist waveguides and thin-film silicon nitride (SiN)/lithium niobate (LN). By carefully designing octave-separating bound states in the continuum (BICs) for the nonlinear interacting waves in such a hybrid structure, we have simultaneously optimized the losses for both fundamental frequency (FF) and second harmonic (SH) waves and achieved modal phasing matching and maximized the nonlinear modal overlap between the FF and SH waves, which results in an experimental conversion efficiency up to 4.05% W^-1cm^-2. Our work provides a versatile and fabrication-friendly platform to explore on-chip nonlinear optical processes with high efficiency in the context of nanophotonics and quantum optics.

Riemann-Encircling Exceptional Points for Efficient Asymmetric Polarization-Locked Devices

Dynamically encircling exceptional points (EPs) have unveiled intriguing chiral dynamics in photonics. However, the traditional approach based on an open manifold of Hamiltonian parameter space fails to explore trajectories that pass through an infinite boundary. Here, by mapping the full parameter space onto a closed manifold of the Riemann sphere, we introduce a framework to describe encircling-EP loops. We demonstrate that an encircling trajectory crossing the north vertex can realize near-unity asymmetric transmission. An efficient gain-free, broadband asymmetric polarization-locked device is realized by mapping the encircling path onto L-shaped silicon waveguides.

Reconfigurable chiral exceptional point and tunable non-reciprocity in a non-Hermitian system with phase-change material

Non-Hermitian optics has emerged as a feasible and versatile platform to explore many extraordinary wave phenomena and novel applications. However, owing to ineluctable systematic errors, the constructed non-Hermitian phenomena could be easily broken, thus leading to a compromising performance in practice. Here we theoretically proposed a dynamically tunable mechanism through GST-based phase-change material (PCM) to achieve a reconfigurable non-Hermitian system, which is robust to access the chiral exceptional point (EP). Assisted by PCM that provides tunable coupling efficiency, the effective Hamiltonian of the studied doubly-coupled-ring-based non-Hermitian system can be effectively modulated to resist the external perturbations, thus enabling the reconfigurable chiral EP and a tunable non-reciprocal transmission. Moreover, such tunable properties are nonvolatile and require no static power consumption. With these superior performances, our findings pave a promising way for reconfigurable non-Hermitian photonic devices, which may find applications in tunable on-chip sensors, isolators and so on.

Exceptional point protected robust on-chip optical logic gates

Optical logic gates are crucial components for information processing and communication using photons. Current optical logic gates typically rely on the light interference principle which requires an accurate manipulation of the dynamical phase of light, making the device quite sensitive to system disturbances such as fabrication errors. Here we introduce non-Hermitian principles into the design of optical logic gates that work in the signal transmission process. We propose an exclusive-or gate for silicon-on-insulator platform by employing the physics in the exceptional point (EP) encirclement process. The EP induced mode switching behavior is applied to manipulate the phase of light which is topologically protected by the energy surface around the EP. As a result, the performance of the device is found to be extremely robust to structural parameter disturbances. The proposed non-Hermitian principle is expected to find applications for other on-chip photonic devices toward high robust performance.

Non-Hermitian Sensing in Photonics and Electronics: A Review

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.

Observation of chiral state transfer without encircling an exceptional point

The adiabatic theorem, a corollary of the Schrödinger equation, manifests itself in a profoundly different way in non-Hermitian arrangements, resulting in counterintuitive state transfer schemes that have no counterpart in closed quantum systems. In particular, the dynamical encirclement of exceptional points (EPs) in parameter space has been shown to lead to a chiral phase accumulation, non-adiabatic jumps and topological mode conversion^1-8. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behaviour is not strictly a result of winding around a non-Hermitian degeneracy⁹. Instead, it seems to be mostly attributed to the non-trivial landscape of the Riemann surfaces, sometimes because of the presence of an EP in the vicinity^9-11. Here, in an effort to bring this counterintuitive aspect of non-Hermitian systems to light and confirm this hypothesis, we provide a set of experiments to directly observe the field evolution and chiral state conversion in an EP-excluding cycle in a slowly varying non-Hermitian system. To do so, a versatile yet unique fibre-based photonic emulator is realized that utilizes the polarization degrees of freedom in a quasi-common-path single-ring arrangement. Our observations may open up new avenues for light manipulation and state conversion, as well as providing a foundation for understanding the intricacies of the adiabatic theorem in non-Hermitian systems.

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Exceptional points (EPs) are degeneracies at which two or more eigenvalues and eigenstates of a physical system coalesce. Dynamically encircling EPs by varying the parameters of a non-Hermitian system enables chiral mode switching, that is, the final state of the system upon a closed loop in parameter space depends on the encircling handedness. In conventional schemes, the parametric evolution during the encircling process has to be sufficiently slow to ensure adiabaticity. Here, we show that fast parametric evolution along the parameter space boundary of the system Hamiltonian can relax this constraint. The proposed scheme enables highly efficient transmission and more compact footprint for asymmetric mode converters. We experimentally demonstrate these principles in a 57 μm-long double-coupled silicon waveguide system, enabling chiral mode switching with near-unity transmission efficiency at 1550 nm. This demonstration paves the way towards high-efficiency and highly integrated chiral mode switching for a wide range of practical applications.

Topological modes in a laser cavity through exceptional state transfer

Shaping the light emission characteristics of laser systems is of great importance in various areas of science and technology. In a typical lasing arrangement, the transverse spatial profile of a laser mode tends to remain self-similar throughout the entire cavity. Going beyond this paradigm, we demonstrate here how to shape a spatially evolving mode such that it faithfully settles into a pair of bi-orthogonal states at the two opposing facets of a laser cavity. This was achieved by purposely designing a structure that allows the lasing mode to encircle a non-Hermitian exceptional point while deliberately avoiding non-adiabatic jumps. The resulting state transfer reflects the unique topology of the associated Riemann surfaces associated with this singularity. Our approach provides a route to developing versatile mode-selective active devices and sheds light on the interesting topological features of exceptional points.

General Rules Governing the Dynamical Encircling of an Arbitrary Number of Exceptional Points

Dynamically encircling an exceptional point in non-Hermitian systems has drawn great attention recently, since a nonadiabatic transition process can occur and lead to intriguing phenomena and applications such as the asymmetric switching of modes. While all previous experiments have been restricted to two-state systems, the dynamics in multistate systems where more complex topology can be formed by exceptional points, is still unknown and associated experiments remain elusive. Here, we propose an on-chip photonic system in which an arbitrary number of exceptional points can be encircled dynamically. We reveal in experiment a robust state-switching rule for multistate systems, and extend it to an infinite-period system in which an exceptional line is encircled with outcomes being located at the Brillouin-zone boundary. The proposed versatile platform is expected to reveal more physics related to multiple exceptional points and exceptional lines, and give rise to applications in multistate non-Hermitian systems.

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

Configurable Phase Transitions in a Topological Thermal Material

Diffusive nature of thermal transportation fundamentally restricts topological characteristics due to the absence of a sufficient parametric space with complex dimensionalities. Here, we create an orthogonal advection space with two advective pairs to reveal the unexplored topological transitions in thermal material. We demonstrate four types of configurable thermal phases, including the nontrivial dynamic-equilibrium distribution, nonchiral steplike π-phase transition, and another two trivial profiles related to the anti-parity-time symmetry nature. Our findings provide a recipe for realizing a topologically robust thermal system under arbitrary perturbations.

Optical Energy-Difference Conservation in a Synthetic Anti-PT-Symmetric System

Anti-parity-time (APT) symmetry is associated with various effects beyond the fundamental limitations implied in the standard Hermitian-Hamiltonian dynamics. Here, we create an optical APT-symmetric system in a synthetic frequency domain using a conventional fiber without intrinsic gain or loss and experimentally reveal photonic APT-symmetric effects, including energy-difference conservation and synchronized power oscillation, which have not yet been confirmed experimentally in the optical domain. The optical fiber-based APT-symmetric system has a long interaction length because of its negligible loss, and the APT-symmetric Hamiltonian is precisely tunable with optical pumping density and phase mismatch. On this basis, we observe the phase transition at exceptional points, energy-difference conservation, and synchronized power oscillation. Our results provide a robust theoretical and experimental framework connecting the emerging non-Hermitian physics with technologically important nonlinear fiber-optic interactions.

Direct Measurement of Topological Properties of an Exceptional Parabola

Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a discriminant number (DN) or the eigenvector holonomy that generates a Berry phase. The multiplicity of topological invariants also makes non-Hermitian topology richer than its Hermitian counterpart. Here, we study a parabola-shaped trajectory formed by EPs with both theory and acoustic experiments. By obtaining both the DNs and Berry phases through the measurement of eigenvalues and eigenfunctions, we show that the EP trajectory endows the parameter space with a nontrivial fundamental group. Our findings not only shed light on exotic non-Hermitian topology but also provide a route for the experimental characterization of non-Hermitian topological invariants.

Suppression and revival of single-cavity lasing induced by polarization-dependent loss

For most photonics devices and systems, loss is desperately averted, since it will increase the power consumption and degrade the performance. However, in some non-Hermitian systems, loss can induce a modal gain when the parity-time symmetry is broken, which offers a new way to manipulate the lasing of active cavities. Here we experimentally observe the counterintuitive phenomenon in a single laser cavity assisted by the polarization-dependent loss. A parity-time symmetric system is constituted by the two orthogonally polarized photonic loops in a single laser cavity, which can guarantee the consistency of two coupling loops. The measured output power of the cavity depends on the cross-polarization loss, which reveals virtually opposite relationships before and after the critical point. It provides a novel, to the best of our knowledge, understanding of polarization loss and shows great potential for lasing manipulation in a single cavity with polarization control.

Sensing and Induced Transparency with a Synthetic Anti-PT Symmetric Optical Resonator

Synthetic dimensions and anti-parity-time (anti-PT) symmetry have been recently proposed and experimentally demonstrated in a single optical resonator. Here, we present the effect of the rotation-induced frequency shift in a synthetic anti-PT symmetric resonator, which enables the realization of a directional rotation sensor with improved sensitivity at an exceptional point (EP) and transparency assisted optical nonreciprocity (TAON) in the symmetry-broken region. The orthogonal rotation of this system results in the direction-independent frequency shift and maintenance of the EP condition even with rotation. Tunable transparency at the EP can thus be fulfilled. Hopefully, the proposed mechanisms will contribute to the development of high-precision rotation sensors and all-optical isolators and make the study of the synthetic anti-PT symmetric EP with rotation possible.

Topological mode switching in modulated structures with dynamic encircling of an exceptional point

Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with time-driven elasticity and viscosity. Topological mode switching with robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour of topological mode switching.

Hamiltonian Hopping for Efficient Chiral Mode Switching in Encircling Exceptional Points

Dynamically encircling exceptional points (EPs) can lead to chiral mode switching as the system parameters are varied along a path that encircles EP. However, conventional encircling protocols result in low transmittance due to path-dependent losses. Here, we present a paradigm to encircle EPs that includes fast Hamiltonian variations on the parameter boundaries, termed Hamiltonian hopping, enabling ultrahigh-efficiency chiral mode switching. This protocol avoids path-dependent loss and allows us to experimentally demonstrate nearly 90% efficiency at 1550 nm in the clockwise direction, overcoming a long-standing challenge of non-Hermitian optical systems and powering up new opportunities for EP physics.

Breaking Anti-PT Symmetry by Spinning a Resonator

Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time (PT) operations, can have entirely real or imaginary eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and topological energy transfer. A merit of anti-PT systems is free of gain, but in recent efforts on making anti-PT devices, nonlinearity is still required. Here, counterintuitively, we show how to achieve anti-PT symmetry and its spontaneous breaking in a linear device by spinning a lossy resonator. Compared with a Hermitian spinning device, significantly enhanced optical isolation and ultrasensitive nanoparticle sensing are achievable in the anti-PT-broken phase. In a broader view, our work provides a new tool to study anti-PT physics, with such a wide range of applications as anti-PT lasers, anti-PT gyroscopes, and anti-PT topological photonics or optomechanics.

Design of a non-Hermitian on-chip mode converter using phase change materials

The introduction of non-Hermiticity into photonics has enabled new design principles for photonic devices. Here we propose the design of a tunable non-Hermitian on-chip mode converter working at telecommunication wavelengths. The key component of the converter is a phase change material, and switching its working state can enable a topological change in the energy surface of the system. The conversion functionality can be realized by dynamically encircling an exceptional point in the parameter space of the device. The device based on this non-Hermitian principle is robust to perturbations of structural parameters and works in broadband. The non-Hermitian principle can be applied for the design of more complex on-chip photonic devices.

Exceptional point in a metal-graphene hybrid metasurface with tunable asymmetric loss

Observation of exceptional points (EPs) in non-Hermitian parity-time (PT) symmetric systems has led to various nontrivial physics and exotic phenomena. Here, a metal-graphene hybrid non-Hermitian metasurface is proposed in the terahertz regime, whose unit cell is composed of two orthogonally oriented split-ring resonators (SRRs) with identical dimensions but only one SRR containing a graphene patch at the gap. An EP in polarization space is theoretically observed at a certain Fermi level of the graphene patch, where the induced asymmetric loss and the coupling strength between the two SRRs match a certain relation predicted by a coupled mode theory. The numerical fittings using the coupled mode theory agree well with the simulations. Besides, an abrupt phase flip around the EP frequency is observed in the transmission in circular polarization basis, which can be very promising in ultra-sensitive sensing applications.

Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

UV-NIR femtosecond laser hybrid lithography for efficient printing of complex on-chip waveguides

We propose UV-IR femtosecond laser hybrid lithography for the efficient printing of complex on-chip waveguides, which offers good performance in terms of processing efficiency and accuracy. With this three-dimensional printing technology, waveguides with complex cross-section shapes, such as owls and kittens, can be easily fabricated with an efficiency increased by 1500% (for ${6}\;\unicode{x00B5} {\rm m}\; \times \;{6}\;\unicode{x00B5} {\rm m}$6µm×6µm). In addition, a circular cross-section waveguide with an extremely low birefringence and complex ${8} \times {8}$8×8 random walk networks were quickly customized, which implies that in the design and preparation of the large-scale optical chips, the proposed maskless method allows for the preparation of highly customized devices.